Sliding Mode Control for 2-D FMII Networked System Under Partially Known Fading Channel Information

This article develops a novel sliding mode control (SMC) scheme for a 2-D Fornasini–Marchesini second (FMII) networked system under 2-D fading channel constraints. First, we characterize the stochastic 2-D fading channel phenomenon by using an extended 2-D hidden Markov process (HMP) and incorporate it into the 2-D FMII system model through a well-posed observation scheme. Then, we establish a 2-D FMII networked system model under the stochastic 2-D fading channel phenomenon. For the 2-D networked system, we address SMC issues under two distinct cases: 1) the transition probability matrix (TPM) and the observation probability matrix (OPM) of HMP are known, and 2) the TPM and OPM are partially known. For the former case, we derive the corresponding criteria for the 2-D SMC synthesis issue by fully considering the global TPM and OPM information. On this basis, SMC comprehensive design is also formulated to handle HMP with partially known TPM and OPM information. Furthermore, we resort to a particle swarm optimization (PSO) algorithm to adaptively tune the 2-D SMC scheme parameters and optimize the 2-D sliding mode domain, simultaneously. Finally, a thermal chemical process example and a metal rolling process example are given to validate the effectiveness of the proposed approaches and algorithm in this article.